Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions

A few-component network of biologically relevant, organic reactions displays bistability and oscillations, without an enzymatic catalyst. Dissipative chemical reaction networks are systems that operate away from equilibrium and exhibit features such as continuous regeneration of components and autonomous regulation. The biological cell is one such out-of-equilibrium chemical network. Until now it has not been possible to recreate this type of dynamic behavior using simple organic molecules relevant to prebiotic Earth. Now, George Whitesides and colleagues demonstrate a few-component system of interacting organic species that, combined into a reaction network, displays autocatalytic and oscillatory features. All of the organic components are relatively simple and do not require enzymatic catalysis to react. Networks of organic chemical reactions are important in life and probably played a central part in its origin1,2,3. Network dynamics regulate cell division4,5,6, circadian rhythms7, nerve impulses8 and chemotaxis9, and guide the development of organisms10. Although out-of-equilibrium networks of chemical reactions have the potential to display emergent network dynamics11 such as spontaneous pattern formation, bistability and periodic oscillations12,13,14, the principles that enable networks of organic reactions to develop complex behaviours are incompletely understood. Here we describe a network of biologically relevant organic reactions (amide formation, thiolate–thioester exchange, thiolate–disulfide interchange and conjugate addition) that displays bistability and oscillations in the concentrations of organic thiols and amides. Oscillations arise from the interaction between three subcomponents of the network: an autocatalytic cycle that generates thiols and amides from thioesters and dialkyl disulfides; a trigger that controls autocatalytic growth; and inhibitory processes that remove activating thiol species that are produced during the autocatalytic cycle. In contrast to previous studies that have demonstrated oscillations and bistability using highly evolved biomolecules (enzymes15 and DNA16,17) or inorganic molecules of questionable biochemical relevance (for example, those used in Belousov–Zhabotinskii-type reactions)18,19, the organic molecules we use are relevant to metabolism and similar to those that might have existed on the early Earth. By using small organic molecules to build a network of organic reactions with autocatalytic, bistable and oscillatory behaviour, we identify principles that explain the ways in which dynamic networks relevant to life could have developed. Modifications of this network will clarify the influence of molecular structure on the dynamics of reaction networks, and may enable the design of biomimetic networks and of synthetic self-regulating and evolving chemical systems.


Networks of organic chemical reactions are important in life and
probably played a central part in its origin [1][2][3] . Network dynamics regulate cell division 4-6 , circadian rhythms 7 , nerve impulses 8 and chemotaxis 9 , and guide the development of organisms 10 . Although out-of-equilibrium networks of chemical reactions have the potential to display emergent network dynamics 11 such as spontaneous pattern formation, bistability and periodic oscillations [12][13][14] , the principles that enable networks of organic reactions to develop complex behaviours are incompletely understood. Here we describe a network of biologically relevant organic reactions (amide formation, thiolate-thioester exchange, thiolate-disulfide interchange and conjugate addition) that displays bistability and oscillations in the concentrations of organic thiols and amides. Oscillations arise from the interaction between three subcomponents of the network: an autocatalytic cycle that generates thiols and amides from thioesters and dialkyl disulfides; a trigger that controls autocatalytic growth; and inhibitory processes that remove activating thiol species that are produced during the autocatalytic cycle. In contrast to previous studies that have demonstrated oscillations and bistability using highly evolved biomolecules (enzymes 15 and DNA 16,17 ) or inorganic molecules of questionable biochemical relevance (for example, those used in Belousov-Zhabotinskii-type reactions) 18,19 , the organic molecules we use are relevant to metabolism and similar to those that might have existed on the early Earth. By using small organic molecules to build a network of organic reactions with autocatalytic, bistable and oscillatory behaviour, we identify principles that explain the ways in which dynamic networks relevant to life could have developed. Modifications of this network will clarify the influence of molecular structure on the dynamics of reaction networks, and may enable the design of biomimetic networks and of synthetic self-regulating and evolving chemical systems. Figure 1 summarizes the network of organic reactions that we used to assemble our model system. All of these reactions are nearly quantitative, and the structure of their reactants can be varied by synthesis to control the rates of reactions. Thiols and thioesters, which are central to these reactions, are important in many biological processes (for example, the formation of disulfide bonds in proteins, transformations involving coenzyme-A, the reduction of oxidized molecules by glutathione 20 , the synthesis of polyketides 21 and the non-ribosomal synthesis of peptides 21 ) and, hence, might represent reactions that enabled life to emerge on the early Earth 22 .
To control the dynamics of these processes, we constructed a modular chemical reaction network, shown schematically in control-theoretic terms 23 in Fig. 1a. A 'trigger' produces an initial chemical signal, and an 'auto-amplifier' amplifies this signal, which may or may not be suppressed by inhibition. To keep the reactions out of equilibriumand, thus, to enable the self-organization of reactions by communication through concentrations of reactants and products-we used a continuously stirred tank reactor (CSTR) to mix reactants and products, while allowing a flux of species into and out of the network over time. A biological cell has some conceptual analogies to a micrometre-scale, diffusively mixed tank reactor. The dynamic behaviour of this system-especially bistability and oscillations-reflects the balances of triggering, auto-amplification and inhibition.
We first constructed a chemical network that is capable of autoamplification using thiols and thioesters (Fig. 1b). The starting components of the network are cystamine (CSSC, 3) and l-alanine ethyl thioester (AlaSEt, 2). Trace amounts of cysteamine (CSH, 1) are generated as follows: AlaSEt slowly hydrolyses, generating alanine (8) and ethanethiol (EtSH, 4); EtSH then reacts with CSSC via thiolate-disulfide interchange 24 , yielding disulfide 6 and CSH. With CSH present, selfamplification occurs through two steps: (i) CSH reacts rapidly with AlaSEt by thiolate-thioester exchange and intramolecular rearrangement (Kent ligation) 25 , yielding two thiols, EtSH and l-alanine mercaptoethyl amide (5); and (ii) these two thiols then undergo thiolatedisulfide interchange with CSSC, yielding two molecules of CSH (and disulfides 6 and 7). Because one molecule of CSH generates two molecules of CSH (a multiplication by two), this network proceeds autocatalytically; hereafter, we refer to it as an 'autocatalytic thiol network' .
We tested this autocatalytic thiol network in a batch reactor (in 500 mM phosphate buffer at pH 7.5). The curve showing the formation of alanine amides (5, 7, 11, 12 and 13) from the reaction of AlaSEt and CSSC has two attributes that are consistent with autocatalysis ( Fig. 2a): it is sigmoidal in shape and the addition of β -mercaptoethanol eliminates the lag period. The results of numerical simulations agree well with experimental results (Extended Data Fig. 1e and Methods). Production of thiols (CSH, 5 and EtSH) also follows autocatalytic kinetics (Extended Data Fig. 1f). Therefore, this system provides a kinetically simple, well-defined autocatalytic reaction-with reactants that can be easily varied structurally by synthesis-based on thiols. Autocatalytic reactions are important in life and play an important part in evolution 26 .
Having developed the autocatalytic reaction system, we focused on developing a set of reactions to control the onset of exponential growth of organic thiols (RSH) (the timing of the trigger). The mechanism outlined in Fig. 1b suggests that a molecule that is capable of rapidly reacting with and, hence, rapidly removing free thiols might delay autocatalytic growth until that molecule is itself depleted by reaction. We hypothesized that the addition of maleimide, which reacts extremely rapidly with thiolates (in comparison to all other rates of reaction in the autocatalytic thiol network), would prevent the formation of 5 and thus prevent auto-amplification of thiols until it is completely consumed. Therefore, in a reaction of AlaSEt, CSSC and maleimide, molecules of EtSH-a free thiol generated by the hydrolysis of AlaSEt-will react with and eventually consume maleimide, at which point the autocatalytic formation of CSH can proceed (Fig. 1b).
To test the ability of maleimide to delay autocatalytic growth, we added 5 mol% of this molecule to a mixture of CSSC and AlaSEt (in batch), and used proton nuclear magnetic resonance ( 1 H NMR) to monitor both the production of alanine amides and the disappearance of maleimide ( Fig. 2b and Extended Data Fig. 3a-c). The production of alanine amides does not proceed until maleimide is consumed, at which point it proceeds autocatalytically.
In a CSTR, autocatalytic reactions can become bistable 27 . In flow systems, bistability often manifests itself through hysteresis; concentrations of reaction intermediates, which are determined by flow rates, do not return to their original values when flow rates are changed and then changed back. To test our reaction network under flow conditions, we constructed a small CSTR and connected it to a spectrophotometer to continuously monitor the total concentration of thiols in the system (Fig. 3, Extended Data Fig. 4). The molecules fed into this CSTR included AlaSEt, CSSC and maleimide.
Numerical simulations suggested that space velocities (defined as the ratio of the flow rate and the reactor volume and given in units of per second) in the range 0.0001-0.01 s −1 would produce hysteresis (see Extended Data Fig. 5a-c). To test the result of these simulations, we monitored the total concentration of thiols during stepwise changes in space velocity within the predicted range. We started from a low flow rate, ramped up to a high flow rate, and then returned to the low flow rate (Fig. 4a). High thiol concentrations generated through self-amplification (of CSH) require the space velocities to be lowered to ≤ 0.0005 s −1 to activate the autocatalytic pathway. The system transitions out of the self-amplifying state when the space velocity is ≥ 0.006 s −1 (Fig. 4b). These limits make qualitative sense: selfamplification requires maleimide to be removed from the CSTR (via reactions with free thiols-or, more exactly, thiolate anions-or via transport out of the CSTR through the outlet port) more rapidly than it is added through the inlet port; the termination of self-amplification, once it has started, requires free thiols to be removed from the CSTR by transport out of the outlet port more rapidly than they are produced (via autocatalysis). An increase in maleimide concentration lowers the limiting flow rates for bistability ( Fig. 4c; Extended Data Fig. 5d-f), as the model predicts. This chemical reaction network illustrates a general way to convert any quadratic autocatalytic system (and perhaps, any system capable of exponential amplification) into a bistable switch by combining this autocatalysis with linear generation and quantitative sequestration of the self-amplifying species.
It has been shown that bistable systems can give rise to oscillations in the presence of an inhibition reaction that slowly (relative to a production reaction) removes the self-amplifying species 13,27,28 . In our system, we chose acrylamide as an inhibitor, because this molecule reacts more slowly with thiols than any other molecule in the reaction network. When we tested this system with acrylamide in batch, it exhibited a single oscillation (that is, one peak) in the concentration of free thiols ( Fig. 2c; Extended Data Fig. 3d, e). NMR analysis (Fig. 2d) shows that the oscillation is not triggered until the maleimide is removed. In addition, it is apparent that AlaSEt is depleted during the oscillation.
Using a combination of numerical simulations and experiments in the CSTR under different flow rates (inputs were AlaSEt, maleimide and acrylamide), we identified conditions under which the addition of acrylamide, present in excess, would produce sustained oscillations in RSH ( Fig. 4d; Extended Data Fig. 6). Each oscillation arises from three steps ( Fig. 4e and Methods): (i) the trigger sets up a delay for auto-amplification of the autocatalytic thiol species; (ii) autocatalytic growth competes with inhibition of thiols by reaction with acrylamide, thus depleting the thioester AlaSEt; (iii) the thioester AlaSEt (and other reagents) is recharged by flow into the CSTR.
To determine how changes in flow rate effect oscillations, we examined the influence of flow rate on the stability, period and amplitude of oscillations. Sustained oscillations occurred for space velocities between 1.4 × 10 −4 s −1 and 2.7 × 10 −4 s −1 (Fig. 4f; Extended Data Fig. 7). Increasing the space velocity to 2.8 × 10 −4 s −1 resulted in a sudden loss of oscillations, and decreasing it to 1.2 × 10 −4 s −1 resulted in damped oscillations. The period increased nonlinearly with space velocity (Fig. 4f); by contrast, the amplitude increased linearly (Fig. 4g).
To explain the trends in period and amplitude of the oscillations, and the nature of the bifurcations at low and high limiting space velocities, we constructed a simple kinetic model (Fig. 4h) that enables qualitative analysis of dynamic behaviours in our oscillating network. This model simplifies the autocatalytic thiol network to bimolecular autocatalytic showing the inputs and outputs of a continuously stirred tank reactor (CSTR). Input (control) parameters include reactor space velocity (flow rate/reactor volume), pH, concentrations of the chemical species, buffer composition and temperature. The output is the thiol concentration [RSH], which changes with time. Inside the CSTR, the trigger is a balance between the generation and the destruction of RSH, which regulates the auto-amplification of RSH. Inhibition and washout remove RSH. b, Reaction schemes describing the elements of the diagram in a that collectively lead to oscillations. (1) Trigger: slow production of RSH by hydrolysis of the thioester, in combination with removal of RSH by reaction with maleimide.
(2) Auto-amplification by autocatalysis: RSH provides a positive feedback loop via thiol-disulfide exchange with CSSC, followed by native chemical ligation with AlaSEt (direct attack of CSSC on AlaSEt is negligible; see Extended Data Fig. 1a Table 1 for details of protonation equilibria). All compounds are represented in their electrically neutral forms for simplicity. Autocatalytic module and autocatalytic species are highlighted in red.  In this set-up, syringe pumps feed reactants to the inlet ports of the CSTR, where they mix and react (red, CSSC in a phosphate buffer of pH 7.5 or 8; orange, AlaSEt in Milli-Q water; blue, maleimide and/or acrylamide in Milli-Q water). For continuous sampling, a tube connected to the outlet port of the CSTR takes the effluent (products and reactants) to a fast in-flow mixing detection chip powered by a μ DC (micro direct current) motor. In this chip, RSH reacts with 5,5′ -dithiobis-(2-nitrobenzoic acid) and forms 4-nitro-3-carboxy-thiophenolate anion, which is detected by absorption at 412 nm using an ultraviolet-visual spectrometer. production of thiols from thioester, and considers the concentrations of CSSC and acrylamide ([CSSC] and [acrylamide]) as constants: , I 0 and S 0 are the concentrations of maleimide and AlaSEt fed into the reactor, respectively, k 1-4 are rate constants and k 0 is the space velocity. Linear stability analysis 13 of this model shows that increasing k 0 from low to high values causes two transitions. First, the system transitions from having a stable focus (damped oscillations) to a stable orbit (sustained oscillations) via an Andronov-Hopf bifurcation 29 . Second, the system transitions from having a stable orbit to a single stable equilibrium (a stable 'node'-an equilibrium in which the system, when perturbed, returns directly to the stable state, as opposed to orbiting around it)

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via a saddle-node or fold bifurcation 29 (see Extended Data Fig. 8a and Methods). Further analysis of this model shows that lowering the concentration of maleimide fed into the reactor (I 0 ) results in a transition from oscillatory to bistable behaviour (see phase plot in Extended Data Fig. 8b). Indeed, experiments with I 0 = 4 mM (all other parameters are the same as those in experiments on oscillations) demonstrated the predicted bistable behaviour of the system at space velocities ranging from 0.0015 s −1 to 0.005 s −1 (Extended Data Fig. 8c).
Our experiments show that we have successfully converted a bistable organic reaction network into an oscillatory network with two experimentally accessible and biologically relevant classes of bifurcations. Systematically designed chemical oscillators are rare. Notable examples are enzymatic 15 , pH 30 , DNA 16,17 and redox oscillators; 28 here, we have demonstrated a class of chemical oscillators based on thiols. This system is unique in that it has characteristics that make it relevant to the discussion of the spontaneous formation of networks from types of molecules relevant to metabolism, to other dynamic networks of organic reactions and perhaps to the origin of life.
This network, which requires only four components (a thioester, a disulfide of a β -aminothiol, a kinetically rapid and irreversible thiol inhibitor, and a slow and irreversible thiol inhibitor), can be varied via structural modifications of the constituent organic molecules; this flexibility in structures offers the potential to explore the evolution and functional design of dynamic networks. The complex behaviour of this simple network of organic reactions illustrates four ideas that are important when considering the emergence of complexity in dynamic networks of chemical reactions. First, our network demonstrates the ability of a simple set of reactants to produce emergent behaviour when feedback is present. Second, it shows 'memory' in the sense that the system is hysteretic and thus encodes information about its past in the concentrations of molecules in the network; in discussions of the origin of life, memory is usually attributed to sequences of bases in replicating molecules of RNA, or its precursors, and alternative forms of memory in dynamic networks broaden its possible origins. Third, our network is compatible with the types of behaviour envisioned 22 in a proposal for a 'thioester' basis for the origin of life; this compatibility reinforces the relevance of this proposal. Finally, our network suggests that the complex regulatory dynamics generally associated with cellular function (for example, threshold-based behaviours and circadian rhythms) might, in principle, have arisen spontaneously before cellular life and, perhaps most importantly, before enzymatic catalysis.
Online Content Methods, along with any additional Extended Data display items and Source Data, are available in the online version of the paper; references unique to these sections appear only in the online paper.

Synthesis.
General. Unless otherwise stated, all starting materials were obtained commercially and were used without further purification. Nuclear magnetic resonance (NMR) spectra were measured on a Varian INOVA I-500 spectrometer at 500 MHz for 1 H and 125.8 MHz for 13 C( 1 H) or on a Varian INOVA I-400 spectrometer at 400 MHz for 1 H. The chemical shifts for 1 H and 13 C are given in parts per million (p.p.m.) relative to TMS, and calibrated using the residual 1 H peak of the solvent; δ = 7.26 for CDCl 3  ) in the batch experiments was determined with Ellman's reagent (5,5′ -dithiobis-2-nitrobenzoic acid) (0.5 mM, phosphate buffer pH 7, 100 mM). A 7.5 μ l sample was added to the Ellman's solution and the absorbance of this solution was measured by ultraviolet-visible spectroscopy after 1 min of incubation. We calculated thiol concentration from absorbance using a calibration curve (Extended Data Fig. 4a). In all plots, we show total concentration of all protonated/deprotonated forms; see Extended Data Table 1 for details of protonation equilibria [31][32][33] . Reaction between AlaSEt and CSSC in the presence of maleimide. We performed experiments as described above. We dissolved CSSC·2HCl (80.5 mM) and maleimide (2.0 mM, 4.0 mM or 6.1 mM) in 0.4 ml of 500 mM phosphate buffer (pH 7.5) in D 2 O and filled the NMR tube with this solution. Thereafter, we dissolved AlaSEt·TFA (107 mM) in 0.3 ml of 500 mM phosphate buffer (pH 7.5) in D 2 O and mixed it with the first solution. In addition to the progress of Kent ligation, we monitored the disappearance of maleimide by following the disappearance of maleimide proton signals in the 1 H NMR spectra. The interval between measurements was 2 min (132-s time intervals considering 12 s of acquisition time).

Reaction between AlaSEt and CSSC in the presence of maleimide and acrylamide.
First, we weighted 8.1 mg of AlaSEt·TFA in a 2-ml glass vial containing a stirring bar. Second, we dissolved CSSC·2HCl (92 mM), maleimide (10 mM) and acrylamide (160 mM or 320 mM) in 0.7 ml of 1 M phosphate buffer (pH 8) in H 2 O. Third, we quickly added the solution to the alanine thioester, shook vigorously, and put it on the magnetic stir plate. 7.5-μ l aliquots of this mixture were used to determine the amount of free thiols at each time point. Flow experiments. We used two types of flow systems: a flow system with the CSTR, mixing and detection chip made completely from polydimethylsiloxane (PDMS) (set-up 1), and a flow system with a hybrid PDMS/glass CSTR and a detection chip with mechanical mixing (set-up 2). Set-up 1 is simple to fabricate, and was used for the bistability experiments. Set-up 2 is harder to fabricate than set-up 1, but it gave a more stable signal than set-up 1; therefore, it was used for the oscillatory experiments. Set-up 1 (for bistability experiments). The CSTR had a volume of 250 μ l, was made of PDMS, used a built-in temperature control channel, and had three separate inlets. We mounted three syringes on a Harvard PhD 2000 syringe pump and fed the CSTR with reactants via the inlet tubing. The temperature control channel was connected to a thermostatic water bath. The outlet of the CSTR was connected to the microfluidic detection chip. This detection chip had two inlets, a mixing channel and a detection chamber that was 150 μ m in height. It served two functions: mixing outgoing flow of the CSTR with Ellman's reagent (5,5′ -dithiobis-(2nitrobenzoic acid)) and providing an optical window for the ultraviolet-visual absorption measurements. The syringe pump supplied the Ellman's reagent via the second inlet (detection chip). Ellman's reagent quantitatively and irreversibly reacted with the free thiols in the reaction mixture releasing an orange-coloured 4-nitro-3-carboxy-thiophenolate that was detected by ultraviolet-visual absorption. To perform ultraviolet-visual absorption measurements, the detection chamber was aligned with collimated light from the Nikon Intensilight C-HGFI and an optic fibre going to the Ocean Optics HP 4000 ultraviolet-visual absorption spectrometer. We detected the intensity of 412-nm light over the course of the experiment. We converted absorbance into the thiol concentration using a calibration curve (Extended Data Fig. 4b). Artefacts from air bubbles passing the detection window were filtered for clarity. All of the pumps were controlled by a MATLAB program that was specifically designed for these experiments (Supplementary Information).

Set-up 2 (for oscillatory experiments).
Detection of the oscillations in the oscillatory experiments required three changes in the fluidic system: using glass instead of PDMS as the material for the CSTR, using active instead of passive mixing during the derivatization step and using a glass flow cell coupled to a Cary 60 ultravioletvisual spectrometer. The glass CSTR ensured no leakage of EtSH by diffusion through PDMS, and also prevented the accumulation of gas bubbles. The active mixing decreased the retention time during the derivatization step, thus reducing the effect of a side reaction between alanine ethyl thioester and Ellman's reagent. (We determined experimentally that, in this set-up, the background reaction with AlaSEt will generate a signal corresponding to an apparent thiol concentration in the range 0.4-0.8 mM for the flow rates and concentrations of reagents that were used in our experiments; apparent rate constant is about 4 × 10 4 times slower than the reported apparent second-order rate constant of the reaction between Ellman's reagent and β -mercaptoethanol at pH 7; ref. 34.) The use of a ultravioletvisual spectrometer eliminated any intensity fluctuations from the light source. Absorbance data were converted into total concentration of free thiols using a calibration curve (Extended Data Fig. 4c, d).
The procedure of making a CSTR with a glass body consisted of three steps. In the first step, we fabricated a glass body. We took a Pasteur pipette, fixed it upsidedown in a drill press and heated it 13 mm from the bottom end using a hand-held burner (MT-51). Interplay between gravity and surface tension resulted in the formation of a glass neck with thick walls. The neck had an internal diameter of 0.9-1 mm. We cut the pipette 8 mm above the neck. To make an outlet connection for tubing, we put the newly made glass chamber upside-down in a Petri dish filled with PDMS, such that PDMS was up to the middle of the neck, and inserted a needle (outer diameter of 0.9 mm) into the neck from the top. A well-defined channel was formed after the PDMS was cured. In the second step, we fabricated a PDMS body with all of the inlet connections and temperature controller. We placed a brass cylinder (diameter, 6. mm; height, 6.82 mm) and a copper tube (one turn around the cylinder) in the Petri dish, and filled the dish with PDMS up to the top of the cylinder such that the top of the cylinder was not covered by PDMS. After curing, we pulled the PDMS out of the dish and removed the cylinder. We cut the inlet channels on the bottom of the PDMS body, and punched holes for the inlet tubing. In the final step, we plasma-bonded the PDMS body to a glass slide, inserted the glass body into the PDMS body (hole from the brass cylinder), sealed the top with additional PDMS and inserted tubing. It is important to insert the glass body as close as possible to the glass slide; however, the elasticity of the PDMS would not allow for full contact between the glass body and glass slide, which left a gap (0.1-0.2 mm) that was exploited to construct inlet channels for the reactor.
To make a fast in-flow mixing chip, we designed the microfluidic device with mixing chamber (diameter, 3 mm; height, 1 mm; volume, 7 μ l) in AutoCAD and 3D-printed moulding master with an Objet Connex 500 3D printer (Stratasys).

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After printing, the master was heated in oven at 70 °C overnight to complete the photo-curing process (otherwise, unreacted components inhibit the PDMS curing in a later step). Using syringe needles, we defined liquid ports (0.9 mm outer diameter) and the placement for the impeller shaft (0.6 mm outer diameter). Thereafter, we used a standard PDMS moulding procedure to cast the chip body. After removal from the master, a syringe needle (0.9 mm outer diameter) was inserted into the mixing chamber and a small impeller was grafted into its end. Then, the PDMS body was plasma-bonded to a glass substrate and the syringe needle was sealed with a small drop of PDMS. We connected the shaft of the impeller to a 5-V micro-d.c. motor running at a speed of about 600 r.p.m. Efficient mixing in the outlet channel of the mixing chip was qualitatively confirmed by visual inspection using water and dye.
To construct the glass flow cell, we drilled two holes (18 mm apart) in the glass slide. Next, we cut two 220-mm-thick cover slips in half and glued pairs of these pieces together using photo-curable glue between two thicker pieces. We glued these doubly thick pieces of glass on the glass slide leaving a 1-mm gap between them (the holes should, of course, point to the gap). Next, we attached the top glass slide (without holes) using glue to create the channel. We removed any leftover glue using nitric acid and sodium hydroxide. We then blocked the ends of the channel using epoxy glue, and we made two rectangular-shaped PDMS pieces with holes for tubing in them. Finally, we plasma-bonded these PDMS pieces on top of the holes to make connections for the channel inlet and outlet tubing. We noted that air bubbles could get stuck in the channel when this chip was used at low flow rates (< 1,000 μ l h −1 ) and so, to prevent bubbles from getting stuck, we stuffed the inlet with crushed glass capillaries-the broken glass pieces created a hydrophilic net that prevented the continuity of a bubble from the PDMS part of the inlet to the channel. Bistability experiments. Four syringes were used: syringe 1 (connected to CSTR), AlaSEt·TFA (92 mM) in water; syringe 2 (connected to CSTR), CSSC·2HCl (184 mM) in 1.127 M phosphate buffer pH 7.5; syringe 3 (connected to CSTR), maleimide (19.3 mM, 38.7 mM or 58 mM) in water; syringe 4 (connected to detection chip), 16.6 mM Ellman's reagent in mixture of MeOH:(NaH 2 PO 4 208 mM) 2:3. Note that Ellman's reagent should be dissolved in MeOH before adding the solution of NaH 2 PO 4 . We used the following flow rates (in μ l min −1 ) to construct hysteresis plots. Numerical modelling. Numerical modelling was done using COPASI 35 and MATLAB programs. MATLAB numerical models for the oscillatory and bistable networks are described below.
The architectures of our bistable and oscillatory networks are outlined in Extended Data Fig. 9a. Under flow conditions, the evolution of the species in the bistable network over time is governed by the following set of ordinary differential equations: AAm is acrylamide; k AAm is the rate constant for all conjugate additions of thiols to acrylamide. We numerically solved these two systems of equations (equations (2) and (3)

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loop (reaction with acrylamide) is described by a first-order reaction with rate constant k 3 ; and third, that the end products can be neglected. With these assumptions, the system of reactions is described by:  (1), reprinted here for convenience: To describe the experimentally observed dependence of the stability of oscillations on space velocity, we analysed the stability of the steady states derived from the following considerations. The steady states are defined by:  The dependence on k 0 for the given rate constants and starting concentrations is then: The dependence of the roots of this cubic equation on k 0 for the region of interest (1 × 10 −4 < k 0 < 4 × 10 −4 ) are shown in the graphs in Extended Data Fig. 8a, b. An analysis of the discriminant of the cubic equation written above shows that solutions of this equation exhibit a fold bifurcation at k 0 = 3.08266724620437 × 10 −4 s −1 , at which two positive solutions collide and disappear. To analyse the stability of the steady states we use the Jacobian matrix (J), and determine the eigenvalues (λ) such that the following is not invertible: where I is the identity matrix. We used a Mathematica script (Supplementary Information; x ≡ k 0 , h 0 ≡ I 0 ) to compute the stability of the steady states.
For k 0 < 3.08266724620437 × 10 −4 s −1 , there is only one physically meaningful (positive and real) steady state. This steady state undergoes a transition from an unstable focus (eigenvalues are complex conjugates with a positive real part) to a stable focus (eigenvalues are complex conjugates with a negative real part) through an Andronov-Hopf bifurcation (referred to hereafter as a Hopf bifurcation). At the Hopf bifurcation, the real part of the eigenvalues should go through zero and computations show that this is indeed the case (see also Extended Data Re(λ 2,3 ) < 0). Supplementary discussions. Bifurcations. A bifurcation point represents a set of conditions for which a smooth change in a control parameter causes a sudden shift in system behaviour. For example, a system might transition from having multiple steady states to having just one, or vice versa (Extended Data Fig. 9b). In our system, as the space velocity is increased to extremely high values, we observe such a transition. The mathematical basis of this transition can be explained by the number of real solutions to a cubic equation (X 3 -X + C = 0). These solutions are a function of control parameter C; as C is increased, two out of three real solutions disappear, indicating a bifurcation point.
Oscillatory systems can undergo bifurcations in which they transition from having a single stable steady state to having one unstable steady state with sustained oscillations. This transition, which is called a Poincare-Andronov-Hopf bifurcation, is apparent in our system. Hysteresis. Hysteresis describes the failure of a system to return to its starting point when an external condition or control parameter is changed and then changed back (Extended Data Fig. 9b). One of the best-known examples of hysteresis is the behaviour of ferromagnetic materials in a magnetic field.
Bistable dynamical systems have at least two stable states (Extended Data Fig. 9b). Without a strong perturbation, the system does not transition from one state to the other. Consequently, when the control parameter is increased from zero, the system will remain at a first set of stable states (the lower solid line in Extended Data Fig. 9b) until a bifurcation point is reached; when the control parameter is again lowered, the system will remain at a second set of stable states (the upper line in Extended Data Fig. 9b) until a bifurcation point is reached. As a result, a hysteresis loop appears. Detailed chemical explanation. Thioesters are carboxylic acid derivatives that can react with various nucleophiles through nucleophilic substitution at their sp 2 carbon. Such a reaction consists of two steps: addition of the nucleophile and loss of the leaving group (for example, thiolate). Our system contains AlaSEt as the thioester and three nucleophiles (hydroxyl, amines and thiolates) with which it can react to form alanine (carboxylic acid), amides and new thioesters (reaction with thiolate is also called thiol-thioester exchange). At pH 7.5-8, reactions with hydroxyls and amines are slow, and reactions with thiolate are fast 36 but reversible (the product is another thioester). Kent ligation relies on this difference in reaction rates. Thiol-thioester exchange goes quickly and is followed by a quick, entropically favourable intramolecular reaction with amine.
In our autocatalytic pathway, CSH reacts with AlaSEt through Kent ligation. This ligation is followed by a fast thiolate-disulfide reaction, making the complete autocatalytic process fast 37 , relative to other reactions in our system.
Two independent pathways result in alanine amides in our system: the direct reaction of amines from CSSC, a noncatalytic reaction, and an autocatalytic pathway through CSH. The ratio between these two pathways is 1:100 or more for our system and is responsible for enabling fine control over the autocatalytic process.
If we run an autocatalytic reaction in a CSTR, then two new processes are added: the continuous addition of thioester and disulfide through the inlet and the removal of thiols and all other products through an outlet (removal of thiols slows amplification). The final concentration of thiols represents a balance between these two processes and the aforementioned reactions.
Maleimide is a conjugated carbonyl derivative, with which nucleophiles can readily react through conjugate addition (that is, addition to the double bond next to the carbonyl group). Maleimide reacts with thiols much faster than with thioesters and disulfides involved in the autocatalytic process and, hence, gives rise to two steady states in a CSTR. In the first state, which has very low concentrations of thiols, maleimide is supplied by flow faster than it is removed by reaction with thiols. In the second state, which has very high concentrations of thiols produced through the autocatalytic pathway, maleimide is consumed by thiols faster than it is supplied by flow.
The addition of acrylamide leads to oscillations. Acrylamide, similarly to maleimide, is a conjugated carbonyl compound that reacts with the same nucleophiles as maleimide. However, its reactivity is several orders of magnitude lower than that of maleimide; as a result, acrylamide is not able to suppress the autocatalytic pathway and is able to remove thiols only when the thioester is depleted. The mechanism by which the slow removal of an activator (that is, the slow removal